/Engine/Source/Runtime/Core/Public/Math/UnrealMathUtility.h
The implementation uses approximations for Exp/Sin/Cos. These are accurate for all sensible values of InUndampedFrequency and DampingRatio so long as InDeltaTime < 1 / InUndampedFrequency (approximately), but are generally well behaved even for larger timesteps etc.
template<class T> static void SpringDamper ( T & InOutValue, T & InOutValueRate, const T & InTargetValue, const T & InTargetValueRate, const float InDeltaTime, const float InUndampedFrequency, const float InDampingRatio )